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Finding the Fourth Proportional to 1,189.54, 1,783.40 and 409.34

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Solution

The fourth proportional to 1,189.54, 1,783.40 and 409.34 is: 613.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,189.54 : 1,783.40 = 409.34 : x
  2. Step 2: Convert to fraction form
    1,189.54/1,783.40 = 409.34/x
  3. Step 3: Cross multiply
    1,189.54x = 1,783.40 × 409.34
  4. Step 4: Simplify right side
    1,189.54x = 730,016.96
  5. Step 5: Solve for x
    x = 730,016.96/1,189.54
  6. Step 6: Final answer
    x = 613.70

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.